There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (-20x - 2{x}^{3} + 4{x}^{5}){\frac{1}{(2 + {x}^{2})}}^{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-20x}{(x^{2} + 2)^{4}} - \frac{2x^{3}}{(x^{2} + 2)^{4}} + \frac{4x^{5}}{(x^{2} + 2)^{4}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-20x}{(x^{2} + 2)^{4}} - \frac{2x^{3}}{(x^{2} + 2)^{4}} + \frac{4x^{5}}{(x^{2} + 2)^{4}}\right)}{dx}\\=&-20(\frac{-4(2x + 0)}{(x^{2} + 2)^{5}})x - \frac{20}{(x^{2} + 2)^{4}} - 2(\frac{-4(2x + 0)}{(x^{2} + 2)^{5}})x^{3} - \frac{2*3x^{2}}{(x^{2} + 2)^{4}} + 4(\frac{-4(2x + 0)}{(x^{2} + 2)^{5}})x^{5} + \frac{4*5x^{4}}{(x^{2} + 2)^{4}}\\=&\frac{160x^{2}}{(x^{2} + 2)^{5}} + \frac{16x^{4}}{(x^{2} + 2)^{5}} - \frac{6x^{2}}{(x^{2} + 2)^{4}} - \frac{32x^{6}}{(x^{2} + 2)^{5}} + \frac{20x^{4}}{(x^{2} + 2)^{4}} - \frac{20}{(x^{2} + 2)^{4}}\\ \end{split}\end{equation} \]

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